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Consider the following system of ODEs: ... The eigenvalues of this simple canonical system are ... . The extremum, ... , is shown as a green dot. If ... , the extremum is an unstable focus. If ... , the extremum is a stable focus. If ... , the dynamic behavior is that of a limit cycle and the critical point is a center. If ... , the trajectories spiral clockwise around the origin. If ... , the trajectories spiral counterclockwise around the origin. The red curve is the parametric plot of the solution of the system of ODEs with an initial condition ... (shown as a cyan dot).

Consider the following system of ODEs: ... The eigenvalues of this simple canonical system are ... . The extremum, ... , is shown as a green dot. If ... , the extremum is an unstable focus. If ... , the extremum is a stable focus. If ... , the dynamic behavior is that of a limit cycle and the critical point is a center. If ... , the trajectories spiral clockwise around the origin. If ... , the trajectories spiral counterclockwise around the origin. The red curve is the parametric plot of the solution of the system of ODEs with an initial condition ... (shown as a cyan dot).